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Quantum simulators with hundreds of qubits and engineerable Hamiltonians have the potential to explore quantum many-body models that are intractable for classical computers. However, learning the simulated Hamiltonian, a prerequisite for any applications of a quantum simulator, remains an outstanding challenge due to the fast increasing time cost with the qubit number and the lack of high-fidelity universal gate operations in the noisy intermediate-scale quantum era. Here we demonstrate the Hamiltonian learning of a two-dimensional ion trap quantum simulator with 300 qubits. We employ global manipulations and single-qubit-resolved state detection to efficiently learn the all-to-all-coupled Ising model Hamiltonian, with the required quantum resources scaling at most linearly with the qubit number. Our work paves the way for wide applications of large-scale ion trap quantum simulators.

We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the dependence on resource-intensive two-qubit gates in conventional gate-based methods. We apply HEA-TI to state engineering of cluster states and analyze the scaling of required quantum resources. We also apply HEA-TI to solve the ground state problem of chemical molecules $\mathrm{H_{2}}$, $\mathrm{LiH}$ and $\mathrm{F_{2}}$. We numerically analyze the quantum computing resources required to achieve chemical accuracy and examine the performance under realistic experimental noise and statistical fluctuation. The efficiency of this ansatz is shown to be comparable to other commonly used variational ansatzes like UCCSD, with the advantage of substantially easier implementation in the trapped-ion quantum simulator. This approach showcases the hardware-efficient ansatz as a powerful tool for the application of the near-term quantum computer.

Two-dimensional (2D) ion crystals have become a promising way to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates between any ion pairs in a 2D crystal of four ions. We use symmetrically placed crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve an addressing crosstalk error below 0.1%. We design and demonstrate a gate sequence by alternatingly addressing two target ions, making it compatible with any single-ion addressing techniques without crosstalk from multiple addressing beams. We further examine the gate performance versus the micromotion amplitude of the ions and show that its effect can be compensated by a recalibration of the laser intensity without degrading the gate fidelity. Our work paves the way for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion crystal.

Trapped atomic ions constitute one of the leading physical platforms for building the quantum repeater nodes to realize large-scale quantum networks. In a long-distance trapped-ion quantum network, it is essential to have crosstalk-free dual-type qubits: one type, called the communication qubit, to establish entangling interface with telecom photons; and the other type, called the memory qubit, to store quantum information immune from photon scattering under entangling attempts. Here, we report the first experimental implementation of a telecom-compatible and crosstalk-free quantum network node based on two trapped $^{40}$Ca$^{+}$ ions. The memory qubit is encoded on a long-lived metastable level to avoid crosstalk with the communication qubit encoded in another subspace of the same ion species, and a quantum wavelength conversion module is employed to generate ion-photon entanglement over a $12\,$km fiber in a heralded style. Our work therefore constitutes an important step towards the realization of quantum repeaters and long-distance quantum networks., Comment: 12 pages, 12 figures

The spin-boson model is a prototypical model for open quantum dynamics. Here we simulate the spin-boson model using a chain of trapped ions where a spin is coupled to a structured reservoir of bosonic modes. We engineer the spectral density of the reservoir by adjusting the ion number, the target ion location, the laser detuning to the phonon sidebands, and the number of frequency components in the laser, and we observe their effects on the collapse and revival of the initially encoded information. Our work demonstrates the ion trap as a powerful platform for simulating open quantum dynamics with complicated reservoir structures.

A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation. As one of the leading physical platforms for quantum information processing, the ion trap has achieved quantum simulation of tens of ions with site-resolved readout in 1D Paul trap, and that of hundreds of ions with global observables in 2D Penning trap. However, integrating these two features into a single system is still very challenging. Here we report the stable trapping of 512 ions in a 2D Wigner crystal and the sideband cooling of their transverse motion. We demonstrate the quantum simulation of long-range quantum Ising models with tunable coupling strengths and patterns, with or without frustration, using 300 ions. Enabled by the site resolution in the single-shot measurement, we observe rich spatial correlation patterns in the quasi-adiabatically prepared ground states, which allows us to verify quantum simulation results by comparing with the calculated collective phonon modes and with classical simulated annealing. We further probe the quench dynamics of the Ising model in a transverse field to demonstrate quantum sampling tasks. Our work paves the way for simulating classically intractable quantum dynamics and for running NISQ algorithms using 2D ion trap quantum simulators.

Generating ion-photon entanglement is a crucial step for scalable trapped-ion quantum networks. To avoid the crosstalk on memory qubits carrying quantum information, it is common to use a different ion species for ion-photon entanglement generation such that the scattered photons are far off-resonant for the memory qubits. However, such a dual-species scheme requires elaborate control of the portion and the location of different ion species, and can be subject to inefficient sympathetic cooling. Here we demonstrate a trapped-ion quantum network node in the dual-type qubit scheme where two types of qubits are encoded in the $S$ and $F$ hyperfine structure levels of ${}^{171}\mathrm{Yb}^+$ ions. We generate ion photon entanglement for the $S$-qubit in a typical timescale of hundreds of milliseconds, and verify its small crosstalk on a nearby $F$-qubit with coherence time above seconds. Our work demonstrates an enabling function of the dual-type qubit scheme for scalable quantum networks.

Quantum many-body scars are non-thermal excited eigenstates of non-integrable Hamiltonians, which could support coherent revival dynamics from special initial states when scars form an equally spaced tower in the energy spectrum. For open quantum systems, engineering many-body scarred dynamics by a controlled coupling to the environment remains largely unexplored. In this paper, we provide a general framework to exactly embed quantum many-body scars into the decoherence-free subspaces of Lindblad master equations. The dissipative scarred dynamics manifest persistent periodic oscillations for generic initial states, and can be practically utilized to prepare scar states with potential quantum metrology applications.We construct the Liouvillian dissipators with the local projectors that annihilate the whole scar towers, and utilize the Hamiltonian part to rotate the undesired states out of the null space of dissipators. We demonstrate our protocol through several typical models hosting many-body scar towers, and propose an experimental scheme to observe the dissipative scarred dynamics based on digital quantum simulations and resetting ancilla qubits., Comment: 7+11 pages, 3+4 figures

Observing nuclear neutrinoless double beta (0vbb) decay would be a revolutionary result in particle physics. Observing such a decay would prove that the neutrinos are their own antiparticles, help to study the absolute mass of neutrinos, explore the origin of their mass, and may explain the matter-antimatter asymmetry in our universe by lepton number violation. We propose developing a time projection chamber (TPC) using high-pressure 82SeF6 gas and top-metal silicon sensors for read-out in the China Jinping Underground Laboratory (CJPL) to search for neutrinoless double beta decay of 82Se, called the NvDEx experiment. Besides being located at CJPL with the world's thickest rock shielding, NvDEx combines the advantages of the high Qbb (2.996 MeV) of 82Se and the TPC's ability to distinguish signal and background events using their different topological characteristics. This makes NvDEx unique, with great potential for low-background and high-sensitivity 0vbb searches. NvDEx-100, a NvDEx experiment phase with 100 kg of SeF6 gas, is being built, with plans to complete installation at CJPL by 2025. This report introduces 0vbb physics, the NvDEx concept and its advantages, and the schematic design of NvDEx-100, its subsystems, and background and sensitivity estimation.

We study how the information flows in many-body dynamics governed by random quantum circuits and discover a rich set of dynamical phase transitions in this information flow. The phase transition points and their critical exponents are established across Clifford and Haar random circuits through finite-size scaling. The flow of both classical and quantum information, measured respectively by Holevo and coherent information, shows similar dynamical phase transition behaviors. We investigate how the phase transitions depend on the initial location of the information and the final probe region, and find ubiquitous behaviors in these transitions, revealing interesting properties about the information propagation and scrambling in this quantum many-body model. Our work underscores rich behaviors of the information flow in large systems with numerous phase transitions, thereby sheds new light on the understanding of quantum many-body dynamics., Comment: 11 pages, 12 figures

Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor networks. We utilize diagrammatic methods and map our problems to the calculations of different partition functions for high-dimensional Ising models with special structures. To address the notorious difficulty in cracking these models, we develop a combinatorial method based on solving the ``puzzle of polyominoes". With this method, we are able to rigorously study statistical properties of the high dimensional random tensor networks. We prove: (a) the entanglement entropy approaches the maximal volume law, except for a small probability that is bounded by an inverse polynomial of the bond dimension; (b) the typicality occurs for the expectation value of a local observable when the bond dimension increases. In addition, we investigate the barren plateaus (i.e., exponentially vanishing gradients) for the high-dimensional tensor network models. We prove that such variational models suffer from barren plateaus for global loss functions, rendering their training processes inefficient in general. Whereas, for local loss functions, we prove that the gradient is independent of the system size (thus no barren plateau occurs), but decays exponentially with the distance between the region where the local observable acts and the site that hosts the derivative parameter. Our results uncover in a rigorous fashion some fundamental properties for variational high-dimensional tensor networks, which paves a way for their future theoretical studies and practical applications., Comment: 19 pages, 8 figures

The Super $\tau$-Charm facility (STCF) is an electron-positron collider proposed by the Chinese particle physics community. It is designed to operate in a center-of-mass energy range from 2 to 7 GeV with a peak luminosity of $0.5\times 10^{35}{\rm cm}^{-2}{\rm s}^{-1}$ or higher. The STCF will produce a data sample about a factor of 100 larger than that by the present $\tau$-Charm factory -- the BEPCII, providing a unique platform for exploring the asymmetry of matter-antimatter (charge-parity violation), in-depth studies of the internal structure of hadrons and the nature of non-perturbative strong interactions, as well as searching for exotic hadrons and physics beyond the Standard Model. The STCF project in China is under development with an extensive R\&D program. This document presents the physics opportunities at the STCF, describes conceptual designs of the STCF detector system, and discusses future plans for detector R\&D and physics case studies.

Storage lifetime and capacity are two important factors to characterize the performance of a quantum memory. Here we report the stable trapping of above 200 ions in a cryogenic setup, and demonstrate the combination of the multi-qubit capacity and long storage lifetime by measuring the coherence time of randomly chosen ions to be on the order of hundreds of milliseconds. We apply composite microwave pulses to manipulate qubit states globally for efficient characterization of different storage units simultaneously, and we compare the performance of the quantum memory with and without the sympathetic cooling laser, thus unambiguously show the necessity of sympathetic cooling for the long-time storage of multiple ionic qubits.

The trapped ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions. In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena such as quantum phase transition, localization, thermalization and information propagation. For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters. Here we report the quantum simulation of a long-range transverse-field Ising model using up to 61 ions and probe the critical behavior of its quantum phase transition through the Kibble-Zurek mechanism. By calibrating and verifying the coupling coefficients, we realize the same model for increasing ion numbers, so as to extract a critical exponent free of the finite size effect. For ferromagnetic interaction, our experimental result agrees well with the previous numerical predictions. As for the anti-ferromagnetic case, signals are too weak to fit a critical exponent due to the frustration in the interaction, but still consistent with the theory.

We propose a scalable design of entangling quantum gates for large ion crystals with the following desirable features: 1) The gate design is universal and applicable for large ion crystals of arbitrary sizes; 2) The gate has no speed limitation and can work outside of the Lamb-Dicke region; 3) The gate operates by driving from either continuous-wave or pulsed laser beams; 4) The gate is insensitive to slow variation of the laser optical phase and works under a thermal state for the ions' motion; 5) The intrinsic gate infidelity can be reduced to a level well below the threshold for fault-tolerant quantum computation under realistic experimental parameters. Different from the previous gate schemes, here we propose a gate design based on driving of the local oscillation mode of the ions instead of the collective normal modes and develop a formalism based on the Heisenberg equations to deal with the many-body quantum dynamics outside of the Lamb-Dicke region., Comment: 5 pages

Jaynes-Cummings-Hubbard (JCH) model is a fundamental many-body model for light-matter interaction. As a leading platform for quantum simulation, the trapped ion system has realized the JCH model for two to three ions. Here we report the quantum simulation of the JCH model using up to 32 ions. We verify the simulation results even for large ion numbers by engineering low excitations and thus low effective dimensions; then we extend to 32 excitations for an effective dimension of $2^{77}$, which is difficult for classical computers. By regarding the phonon modes as baths, we explore Markovian or non-Markovian spin dynamics in different parameter regimes of the JCH model, similar to quantum emitters in a structured photonic environment. We further examine the dependence of the non-Markovian dynamics on the effective Hilbert space dimension. Our work demonstrates the trapped ion system as a powerful quantum simulator for many-body physics and open quantum systems.

Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system., Comment: 8 pages, 4 figures

Information in a chaotic quantum system will scramble across the system, preventing any local measurement from reconstructing it. The scrambling dynamics is key to understanding a wide range of quantum many-body systems. Here we use Holevo information to quantify the scrambling dynamics, which shows a phase-transition-like behavior. When applying long random Clifford circuits to a large system, no information can be recovered from a subsystem of less than half the system size. When exceeding half the system size, the amount of stored information grows by two bits of classical information per qubit until saturation through another sharp unanalytical change. We also study critical behavior near the transition points. Finally, we use coherent information to quantify the scrambling of quantum information in the system, which shows similar phase-transition-like behavior., Comment: 10 pages, 5 figures

Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain unexplored. Here we simulate the dynamics of a 2D Weyl particle. We show the linear dispersion relation of the free particle and the discrete Landau levels in a magnetic field, and we explicitly measure the spatial and spin dynamics from which the conservation of helicity and properties of antiparticles can be verified. Our work extends the application of an ion trap quantum simulator in particle physics with the additional spatial and spin degrees of freedom.

Ising model is a widely studied class of models in quantum computation. In this paper we investigate the computational characteristics of the random field Ising model (RFIM) with long-range interactions that decays as an inverse polynomial of distance, which can be achieved in current ion trap system. We prove that for an RFIM with long-range interaction embedded on a 2-dimensional plane, solving its ground state is NP-complete for all diminishing exponent, and prove that the 1-dimensional RFIM with long-range interaction can be efficiently approximated when the interaction decays fast enough.

Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources both in quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion's spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average phonon number of the oscillation mode is used as the order parameter to provide evidence for the DPT. Our work highlights the suitability of trapped ions for simulating open quantum systems and shall facilitate further investigations of DPT with various dissipation terms.

Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and higher-order topology. However, as a minimum model of fragile topology, the two-dimensional topological Euler insulator consisting of three bands remains a significant challenge to be implemented in experiments. Here, we experimentally realize a three-band Hamiltonian to simulate a topological Euler insulator with a trapped-ion quantum simulator. Through quantum state tomography, we successfully evaluate the Euler class, Wilson loop flow and entanglement spectra to show the topological properties of the Hamiltonian. We also measure the Berry phases of the lowest energy band, illustrating the existence of four crossing points protected by the Euler class. The flexibility of the trapped-ion quantum simulator further allows us to probe dynamical topological features including skyrmion-antiskyrmion pairs and Hopf links in momentum-time space from quench dynamics. Our results show the advantage of quantum simulation technologies for studying exotic topological phases and open a new avenue for investigating fragile topological phases in experiments., Comment: 19 pages including appendixes, 12 figures

Quantum many-body scarred systems host special non-thermal eigenstates that support periodic revival dynamics and weakly break the ergodicity. Here, we study the quantum information scrambling dynamics in quantum many-body scarred systems, with a focus on the "PXP" model. We use the out-of-time-ordered correlator (OTOC) and Holevo information as measures of the information scrambling, and apply an efficient numerical method based on matrix product operators to compute them up to 41 spins. We find that both the OTOC and Holevo information exhibit a linear light cone and periodic oscillations inside the light cone for initial states within the scarred subspace, which is in sharp contrast to thermal or many-body localized systems. The periodic revivals of OTOCs and Holevo information signify unusual breakdown of quantum chaos and are not equivalent to the revival dynamics of state fidelity or local observables studied in the previous literature. To explain the formation of the linear light cone structure, we provide a perturbation-type calculation based on a phenomenological model. In addition, we demonstrate that the OTOC and Holevo information dynamics of the "PXP" model can be measured using the Rydberg-atom quantum simulators with current experimental technologies, and numerically identify the measurable signatures using experimental parameters., Comment: 14 pages, 11 figures

Capsule networks, which incorporate the paradigms of connectionism and symbolism, have brought fresh insights into artificial intelligence. The capsule, as the building block of capsule networks, is a group of neurons represented by a vector to encode different features of an entity. The information is extracted hierarchically through capsule layers via routing algorithms. Here, we introduce a quantum capsule network (dubbed QCapsNet) together with an efficient quantum dynamic routing algorithm. To benchmark the performance of the QCapsNet, we carry out extensive numerical simulations on the classification of handwritten digits and symmetry-protected topological phases, and show that the QCapsNet can achieve an enhanced accuracy and outperform conventional quantum classifiers evidently. We further unpack the output capsule state and find that a particular subspace may correspond to a human-understandable feature of the input data, which indicates the potential explainability of such networks. Our work reveals an intriguing prospect of quantum capsule networks in quantum machine learning, which may provide a valuable guide towards explainable quantum artificial intelligence., Comment: 7 pages (main text) + 8 pages (supplementary information), 8 figures

Non-Hermiticity has widespread applications in quantum physics. It brings about distinct topological phases without Hermitian counterparts, and gives rise to the fundamental challenge of phase classification from both theoretical and experimental aspects. Here we report the first experimental demonstration of unsupervised learning of non-Hermitian topological phases with the nitrogen-vacancy center platform. In particular, we implement the non-Hermitian twister model, which hosts peculiar knotted topological phases, with a solid-state quantum simulator consisting of an electron spin and a nearby $^{13}$C nuclear spin in a nitrogen-vacancy center in diamond. By tuning the microwave pulses, we efficiently generate a set of experimental data without phase labels. Furthermore, based on the diffusion map method, we cluster this set of experimental raw data into three different knotted phases in an unsupervised fashion without a priori knowledge of the system, which is in sharp contrast to the previously implemented supervised learning phases of matter. Our results showcase the intriguing potential for autonomous classification of exotic unknown topological phases with experimental raw data., Comment: 7+20 pages

Quantum simulation elucidates properties of quantum many-body systems by mapping its Hamiltonian to a better-controlled system. Being less stringent than a universal quantum computer, noisy small- and intermediate-scale quantum simulators have successfully demonstrated qualitative behavior such as phase transition, localization and thermalization which are insensitive to imperfections in the engineered Hamiltonian. For more complicated features like quantum information scrambling, higher controllability will be desired to simulate both the forward and the backward time evolutions and to diagnose experimental errors, which has only been achieved for discrete gates. Here, we study the verified scrambling in a 1D spin chain by an analogue superconducting quantum simulator with the signs and values of individual driving and coupling terms fully controllable. We measure the temporal and spatial patterns of out-of-time ordered correlators (OTOC) by engineering opposite Hamiltonians on two subsystems, with the Hamiltonian mismatch and the decoherence extracted quantitatively from the scrambling dynamics. Our work demonstrates the superconducting system as a powerful quantum simulator.

Classification and identification of different phases and the transitions between them is a central task in condensed matter physics. Machine learning, which has achieved dramatic success in a wide range of applications, holds the promise to bring unprecedented perspectives for this challenging task. However, despite the exciting progress made along this direction, the reliability of machine-learning approaches likewise demands further investigation. Here, with the nitrogen-vacancy center platform, we report the first proof-of-principle experimental demonstration of adversarial examples in learning topological phases. We show that, after adding a tiny amount of carefully-designed perturbations, the experimentally observed adversarial examples can successfully deceive a splendid phase classifier, whose prediction accuracy is larger than $99.2\%$ on legitimate samples, with a notably high confidence. Our results explicitly showcase the crucial vulnerability aspect of applying machine learning techniques in classifying phases of matter, which provides an indispensable guide for future studies in this interdisciplinary field.

Tensor networks are efficient representations of high-dimensional tensors with widespread applications in quantum many-body physics. Recently, they have been adapted to the field of machine learning, giving rise to an emergent research frontier that has attracted considerable attention. Here, we study the trainability of tensor-network based machine learning models by exploring the landscapes of different loss functions, with a focus on the matrix product states (also called tensor trains) architecture. In particular, we rigorously prove that barren plateaus (i.e., exponentially vanishing gradients) prevail in the training process of the machine learning algorithms with global loss functions. Whereas, for local loss functions the gradients with respect to variational parameters near the local observables do not vanish as the system size increases. Therefore, the barren plateaus are absent in this case and the corresponding models could be efficiently trainable. Our results reveal a crucial aspect of tensor-network based machine learning in a rigorous fashion, which provide a valuable guide for both practical applications and theoretical studies in the future., Comment: 7+21 pages

Trapped ions constitute one of the most promising systems for implementing quantum computing and networking. For large-scale ion-trap-based quantum computers and networks, it is critical to have two types of qubits, one for computation and storage, while the other for auxiliary operations like runtime qubit detection, sympathetic cooling, and repetitive entanglement generation through photon links. Dual-type qubits have previously been realized in hybrid systems using two ion species, which, however, introduces significant experimental challenges for laser setup, gate operations as well as the control of the fraction and positioning of each qubit type within an ion crystal. Here we solve these problems by implementing two coherently-convertible qubit types using the same ion species. We encode the qubits into two pairs of clock states of the 171Yb+ ions, and achieve fast and high-fidelity conversion between the two types using narrow-band lasers. We further demonstrate that operations on one qubit type, including sympathetic laser cooling, gates and qubit detection, have crosstalk errors less than 0.03% on the other type, well below the error threshold for fault-tolerant quantum computing. Our work showcases the feasibility and advantages of using coherently convertible dual-type qubits with the same ion species for future large-scale quantum computing and networking., Comment: 9 pages, 7 figures

Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the control parameter of the Hamiltonian is scanned across a quantum critical point. Recently it has been realized that a QPT can also occur in a simple system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report the first experimental demonstration of a QPT in the QRM using a single trapped ion. We measure the average spin-up state population of the ion and the average phonon number in its spatial oscillation mode as two order parameters and observe the clear evidences of the phase transition via slow quench of the coupling between the ion and its spatial motion. An experimental probe of the phase transitions in a fundamental quantum optics model without imposing the thermodynamic limit opens up a new window for the controlled study of QPTs and quantum critical phenomena., Comment: 15 pages, 9 figures

A new $\alpha$-emitting isotope $^{214}$U, produced by fusion-evaporation reaction $^{182}$W($^{36}$Ar, 4n)$^{214}$U, was identified by employing the gas-filled recoil separator SHANS and recoil-$\alpha$ correlation technique. More precise $\alpha$-decay properties of even-even nuclei $^{216,218}$U were also measured in reactions of $^{40}$Ar, $^{40}$Ca with $^{180, 182, 184}$W targets. By combining the experimental data, improved $\alpha$-decay reduced widths $\delta^2$ for the even-even Po--Pu nuclei in the vicinity of magic neutron number $N=126$ were deduced. Their systematic trends are discussed in terms of $N_{p}N_{n}$ scheme in order to study the influence of proton-neutron interaction on $\alpha$ decay in this region of nuclei. It is strikingly found that the reduced widths of $^{214,216}$U are significantly enhanced by a factor of two as compared with the $N_{p}N_{n}$ systematics for the $84 \leq Z \leq 90$ and $N<126$ even-even nuclei. The abnormal enhancement is interpreted by the strong monopole interaction between the valence protons and neutrons occupying the $\pi 1f_{7/2}$ and $\nu 1f_{5/2}$ spin-orbit partner orbits, which is supported by a large-scale shell model calculation.

Cross-resonance (CR) gate has emerged as a promising scheme for fault-tolerant quantum computation with fixed-frequency qubits. We experimentally implement entangling CR gate by using a microwave-only control in a tunable coupling superconducting circuit, where the tunable coupler provides extra degrees of freedom to verify optimal condition for constructing CR gate. By developing three-qubit CR Hamiltonian tomography protocol, we systematically investigate the dependency of gate fidelities on spurious qubit interactions and present the first experimental approach to the evaluation of the perturbation impact arising from spectator qubits. Our results reveal that the spectator qubits lead to reductions in CR gate fidelity dependent on ZZ interaction and particular frequency detunings between spectator and gate qubits, demonstrating a more serious impact from the target spectator than from the control spectator. Our experiments uncover optimal CR operation regime and provide insight into an improvement of the CR gate by suppression of unwanted qubit interactions.

Non-Hermitian topological phases exhibit a number of exotic features that have no Hermitian counterparts, including the skin effect and breakdown of the conventional bulk-boundary correspondence. Here, we implement the non-Hermitian Su-Schrieffer-Heeger (SSH) Hamiltonian, which is a prototypical model for studying non-Hermitian topological phases, with a solid-state quantum simulator consisting of an electron spin and a $^{13}$C nuclear spin in a nitrogen-vacancy (NV) center in a diamond. By employing a dilation method, we realize the desired non-unitary dynamics for the electron spin and map out its spin texture in the momentum space, from which the corresponding topological invariant can be obtained directly. Our result paves the way for further exploiting and understanding the intriguing properties of non-Hermitian topological phases with solid-state spins or other quantum simulation platforms., Comment: 10 pages, 6 figures